Mr. Mime, The Barrier Pokémon. Emanations from its fingertips solidify the air into invisible walls that repel even harsh attacks. It is adept at conning people. It is said to be able to create walls out of thin air by miming.It shapes an invisible wall in midair by minutely vibrating its fingertips to stop molecules in the air.It is a pantomime expert that can create invisible but solid walls using miming gestures. A skilled mime from birth, it gains the ability to create invisible objects as it matures. Its fingertips emit a peculiar force field that hardens air to create an actual wall.

Overview

Mr. Mime is probably the strangest Pokemon to have ever been created. Is it even a Pokemon? It looks like a slightly upsetting man in makeup who looks suspiciously like "Mr Friend" from that old episode of the Rugrats. Oh did I mention it's a fairy type? Yeah apparently mimes are fairies. Mr. Mime's stats are overall pretty bad. Its movepool is solid but it can't really make use of most of it. Mr. Mime's 3D model is also by far the most horrifying thing to ever be implemented in a Pokemon game. Seriously just look at it. Ugh. Positives
- Good movepool. It learns everything it needs to carve out some basic usage even in standard play.
- Soundproof + Baton Pass means it is almost a staple on all Baton Pass teams for its ability to block Perish Song.
- Barrier Ball was the best Pokemon Stadium 2 minigame.

Negatives
- Defenses are very bad. Don't let the high Special Defense stat fool you... the low HP means that you take hits about as well as Sunflora.
- Fairy typing doesn't benefit Mr. Mime like it does others. Bad durability means Dragons still beat you. Mr. Mime doesn't even get Moonblast.
- Incredible Physical movepool yet less attack than Poliwag.
- Mr. Mime gets a ton of support moves but really lacks the typing and stats to use them.

Abilities

Soundproof: Unaffected by sound moves. If this Pokémon switches out with Baton Pass, Perish Song against the switched out will not be nullified. Soundproof allows Mr. Mime to hard counter Perish Song users when it is part of a Baton Pass chain. It is the only Soundproof Pokemon with Baton Pass, and thus it is irreplaceable.Filter: Damage by super-effective moves is reduced by 25%. This ability is great, and it would be on almost anything else. However Mr. Mime's defenses are pitiful. If you are hit with a Super Effective move you will probably not survive it regardless of Filter.
Hidden Ability (Available): Technician: Moves with a base power of 60 or less raise to 1.5 times. Mr. Mime has very little use for Technician. It gets Shock Wave, Magical Leaf, and Hidden Power but not much else.

Mr. Mime does literally one thing well, and that is Baton Pass on a dedicated Baton Pass team. This Mr. Mime is not good at "quick passes" in which you Baton Pass a few boosts immediately to a single Pokemon and sweep. Pokemon like Gorebyss and Smeargle sending off Shell Smashes are better at that. Full Baton Pass teams consist of 6 Pokemon that all run Baton Pass. They usually start off with a Ninjask to pass some speed followed by a few defense and Calm Mind boosters that all lead to a Stored Power Espeon sweep. These teams usually look something like Ninjask / Espeon / Mr. Mime / Mawile / Vaporeon / filler and are pretty difficult to stop once they get up an unbroken Substitute. Mr. Mime is a key member here because it can switch in on Perish Song and completely block it with Soundproof. Soundproof also blocks Roar which is helpful against defensive Heatran. Throwing all your EVs into HP and Defense allows you to Barrier as a Scizor switches in, sponge a super effective Banded Bullet Punch as you Barrier a second time, and have just enough HP leftover to Baton Pass +4 Defense away to something else on the Baton Pass chain. If Barrier isn't your thing you can also try Encore. Encore lets you set up all over anything foolish enough to try and setup alongside you or trying to use status moves. Taunt also works, though on Baton Pass teams you may be best off just Subbing and boosting stats on your free turns.

Rainbow the clown has transformed into... Mr. Mime!... ? No? No one else remembers that episode of the Powerpuff Girls? If you don't want to try a Defensive Baton Passer you can attempt to go the offensive route with Mr. Mime. Shadow Ball + Dazzling Gleam hits every Pokemon in the game neutral except that new Normal / Fire lion thing. While Mr. Mime's base 100 Special Attack is decent at best it will sting after a Nasty Plot. The key to this set is Baton Pass. If your opponent ends up scaring away Mr. Mime with a Blissey or Ferrothorn you can Baton Pass your boosts away to something else.

Other Options

Choice Specs + Trick, Thunderbolt, Focus Blast, Psyshock, Energy Ball, Future Sight, Power Split, Reflect / Light Screen, and Healing Wish.
Mr. Mime has the movepool to run Choice Specs + Trick, but not really the sheer crushing power that something like Latios has.Thunderbolt is okay to hit Gyarados extremely hard. Water types besides Rotom Wash aren't as common as they used to be however.Focus Blast can tear through Tyranitar, Heatran, and Ferrothorn but is unreliable and doesn't afford much coverage over your other moves.
If you get tired of Fairy / Ghost coverage and really dislike Blissey you can try Psyshock to take a chunk out of the pink blobs and destroy Tentacruel.Energy Ball hits Rotom Wash and Gastrodon... but nothing else.Future Sight has 120 base power and 100% accuracy now. Use Future Sight, switch out, and attack with something else. Your opponent will end up getting hit by two moves in one turn which if you pick your moves right will usually result in a KO.Power Split works well off Mr. Mime's low Attack, basically functioning like Reflect.
Speaking of Reflect (and Light Screen) Mr. Mime does learn both moves (obviously). Its defenses are bad and Mr. Mime is kind of slow, so it isn't very good at it despite its entire design being based off invisible walls.
The last option is Healing Wish. While Healing Wish is an amazing move Mr. Mime is built to Baton Pass its terrible payload to a teammate, not sacrifice itself. If you want to use Healing Wish use Latias or Jirachi.

Double & Triple Battle Options

If you want to use a bad Psychic in Doubles and Triples you might as well use something else. Even Delphox might manage a KO or two with Heat Wave before Mr. Mime does anything notable.

Countering Mr. Mime

Hit "Pokemon". Click "Scizor". Use "Bullet Punch". Mr. Mime is now gone.
Alternatively if you lack Scizor just hitting Mr. Mime with any strong physical move will beat it. Mr. Mime is very slow so you can usually hit it first before it does anything. Mr. Mime is usually part of a Baton Pass chain so your bigger issue is beating the chain, not just Mr. Mime as Mr. Mime will just Baton Pass to another team member at the first sign of trouble. You can try Taunt but generally the Baton Pass team will run Espeon which completely nullifies Taunt with Magic Bounce. Beating Baton Pass requires hitting extremely hard as quickly as possible. If your opponent can get a few Defense boosts you might as well quit because you are going to lose. Sableye hard counters basically every Baton Pass team as it has priority Taunt which allows you to use Taunt before they can Baton Pass to Espeon. Sableye also beats Espeon one on one if for some reason they still manage to Baton Pass.
It's difficult to explain how to beat Baton Pass teams because they're very rare. So rare that you shouldn't really worry about them when you're building your team. Actually beating Mr. Mime outside of a Baton Pass chain is easy. Besides Scizor you can take it out with basically any physical attacker. Lucario, Charizard X, Talonflame, Mamoswine, Excadrill, Gyarados, Azumarill etc. All you have to watch out for is Mr. Mime Baton Passing to something else. However this isn't nearly as dangerous as you might think as without a full Baton Pass team the Baton Pass recipient won't have any speed boosts to sweep with.
In short beating Mr. Mime is probably one of the easiest things you will ever have to do. However if you face Mr. Mime with the full support of a Baton Pass team... good luck.